As a interdisciplinary field, one's educational background can vary while still maintaining marketability within the job market.

Your degrees are relevant in that you have an academic background in technical and non-technical fields, which one could argue gives you the ability to synthesize the two. This is a strength in the UX field.

However, I would propose that in a diverse and emerging field such as this, the academic world has not caught up to industry and is not able to offer a standard curriculum.

Consequently your value as a prospective employee is related to what your have proven you can do, or in the case of an entry level job, what potential you can demonstrate.

This is a completely unscientific poll however I asked a question on Polar about what matters more, professional experience or an advanced degree.

As of 12/27/12 the results stood at 195-6 in favor of experience.

If you are looking to try to get into the field, look at your current projects (if you are already in the professional world) or look at your current course work (if you are still in university) and ask yourself if there is a UX angle and work to creatively incorporate UX principles into the project. Highlight this work in your resume and be able to explain to a potential employer how including UX in the project benefited the organization. This will demonstrate independence, initiative, and resourcefulness which are all positive qualities.

UX is a field that lies in the overlap between many other fields. It involves having a working understanding of many different subjects and taking them into account.

As such, computer science and marketing are some of the more useful fields, but you will have to work to learn about many more. In fact, you should always be learning and will never have finished your education.

I would first ask WHY you want to get into UX? What is attractive to UX that you thought you would find in the other fields?

UX is really about asking WHY? Why do people do the things they do? This means more then just working with an app. But, how they do things outside of that app. How can you translate what they're doing to the app or solution you've been asked to architect?

UX is mostly psychology with the rest in implementation. You have to love UX and want to be a champion for the user. The days of a company just building an app and and engineer saying somewhere "well, they can figure it out" just don't work. UX is in everything. The shower head you using in the morning, the toaster, your cars dashboard etc. UX is all around us.

UX takes time. In all due honesty. Going after another degree will not land you a great UX position. Your skills and years of actually doing the work will. Learning UX processes is one thing. Putting them into practice on a $30M+ global project is something totally different.

Some of the things you should get to know are.

Information Architecture

Wire Frames

Heuristic Evaluations

Cognitive Analysis

User Research

Adobe Suite

Some front-end code. At a min Html, CSS, Jquery (you already have this from CS)

WHY? Learn how to ask this of everything you see. What was the designer trying to get the user to do?

I also happen to run the largest group on the net for UX professionals on Linkedin called User Experience. Ask the same question there and you'll get a TON of answers from some of the industries leaders.